some kind of opinion, as a basis for speculation. In the first class are included questions, arising in every province of natural philosophy, which our reason can never solve, but which may yet be regarded as positive, because it is conceivable that they would be manageable by a better organized intelligence, qualified for a more complete investigation and more powerful deductions. In such a case, we may select such artifices as are suggested by the genius of the science concerned, with due care that they shall aid, and not impede, the accretion of real knowledge. Of this kind is the hypothesis spontaneously adopted in physics, relative to the molecular constitution of bodies; and the device of dualism which I suggested in chemistry, in aid of the higher speculations of the science. In the second case, it is only necessary to apply the theory of hypotheses, sufficiently treated of in connection with physics; and which, when duly applied to practice without abuse, cannot but improve the cultivation of genuine knowledge. Thus we find the philosophical view of the study of natural laws to be, that that study represents to us the external world, by satisfying the essential inclinations of our reason, as far as is allowed by the precision prescribed by our practical needs. Qur statical laws correspond to this instinctive predilection for order and agreement; and our dynamical laws accord with our irresistible tendency to believe in the perpetuity of any return once established.

We have now only to consider the institution and gradual development of the positive method.

The whole procedure of our reason affords promise that the Extension of positive philosophy will, in course of time, comprethe method. hend all subjects of human thought; not only science, but art,-æsthetic and technical. Yet, while keeping this prospect in view, we must abide by the double preparatory division which has thus far existed;-between speculation and practice first; and then between scientific and æsthetic contemplation. We have seen that these divisions date from the polytheistic period; the first becoming visible under the theocratic phase, and the other under the Greek system; and both having persisted to this day, notwithstanding the growing importance of their mutual relations. In all the six provinces of knowledge, we find the first, condition of mental progress to be the independence of theory, as no conceptions could have been formed if the theoretical point of view had been inseparable from the practical. We see too how both must have entire freedom,-the theoretical spirit to retire into its condition of analytical abstraction, and the practical to occupy itself with specialities. If either repressed the other, the consequences would be fatal to progress: the practical supremacy would extinguish those tendencies which are already too weak; and the theoretical would exclude reality by preventing any practical operation from being completed. Our mental habits, generated by the old philos

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ophy, induce us to exaggerate the value of à priori considerations. They are very efficacious if wisely instituted and conducted; but the first condition of their utility is, that they should be applied by the practical spirit in each concrete case, the scientific data being merely comprehended among the elements of the special combination employed. Any greater subordination of the practical to the theoretical than this, could lead to nothing but hopeless disturbance. The nature of modern civilization tends to obviate such disturbance, by establishing the division in more and more clearness; and now the sociological spirit entirely consolidates it, by extending it to political conditions, in the way that we have seen. The division between the two kinds of contemplation, the scientific and the aesthetic,-is much less disputed, though it is less marked. Even when imagination ruled in philosophy, the poetical spirit, in its utmost freedom, always recognized its subordination to the philosophical spirit, through the fundamental relation which connects the sense of the beautiful with the knowledge of the true, and thereby subjects the ideality of Art to the collective conditions of scientific reality. As reorganization proceeds, their combination will become closer, and especially in practical life,-Art affording to science, in return for a secure basis, not only intellectual solace and moral stimulus, but much reactive aid in perfecting its philosophical character. Under a relative philosophy, Art may be employed as it could not be under an absolute system, in facilitating scientific expression, and even suggesting modes of scientific pursuit. Whatever may be the ulterior value of such a connection, the distinction between the two kinds of contemplation will always be radical, and the more abstract and general will always govern

the less.

Abstract and

concrete

Science.

A more modern, but wholly indispensable division remains to be noticed; that between abstract and concrete science, as established by me through the whole course of this Work. Bacon was the first who saw (and he but indistinctly), that what he called the First Philosophy (because it must form the basis of the whole intellectual system) could result only from an abstract and analytical study of the elementary phenomena which, in varied combination, constitute the existence of natural beings, for the purpose of ascertaining the laws proper to each order of incidents, considered directly and apart from the beings which manifest it. From no clear and express understanding of this distinction, but merely because it was impossible to proceed otherwise, scientific progress has been guided by it for two centuries past: for, as we have seen throughout, concrete science, or natural history, properly so called, could not be even undertaken till abstract science was instituted in regard to all the orders of elementary phenomena concerned; every concrete inquiry involving the combination of the two. Now, it is only in this work, which

first constitutes the final and most important science, that the condition has been fulfilled; and it is therefore not surprising that the great scientific speculations between Bacon's time and ours have been of an abstract character,-the concrete speculations during the same interval having been necessarily impotent: nor can such a forced and empirical observance of the Baconian precept preclude the necessity of the demonstration which discloses the full bearings of the suggestion. Though the creation of Sociology, by completing and systematizing the first philosophy, must soon ensure an adequate treatment of concrete questions, it is not the less important to remember that the institution of the positive method must for ever rest upon the division, without which the two already pointed out would be altogether insufficient. This division constitutes in fact the most powerful and delicate of all the general devices required by the speculative working out of the positive system. The simplest, most general, and highest point of view attainable by the philosophical spirit has been reached by a gradual process of abstraction, discarding first practical requirements, then æsthetic impressions, and finally, concrete conditions: and if this last, founded on the same logical grounds as the others, had not accrued, to complete their efficacy, the positive philosophy could not have yet existed. In the simplest cases, even those of astronomical phenomena, we have seen that no general law could be established, while bodies were considered in their collective concrete existence, from which it was necessary to detach the leading phenomenon, and then to subject it to abstract examination, which, again, might react on the study of the most complex realities. The grand application of this logical precept is however in the case of sociological theories, from their extreme complexity; and in this province we see what rationality has been established, amidst all the dangers arising from a mass of unorganized learning, by my having put aside all concrete disturbance, in order to seize, in its simplicity, the law of human movement, leaving all apparent anomalies to be reduced to principle afterwards, as in the astronomical case. The maintenance of the division is necessary here for the same reasons as in regard to the two others, under penalty of lapse into such confused views and desultory speculations as we have with so much difficulty escaped from: and if this seems to remove the theoretical view too far from the practical, there will be a compensation in a superior generality, testifying to the necessity of the political and philosophical separation recommended in the last chapter as the basis of modern reorganization.

These are the three stages of successive abstraction, the combination of which determines the gradual institution of the positive method, in a spontaneous manner at first, and afterwards systematically. As the method is neither more nor less than a philosophical extension of popular wisdom to abstract speculation, it is clear that

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its basis, corresponding with that of common sense, admits of no useful dogmatic explanation. If on this ground we decline looking for such dogmatic explanation of the lowest subjects of speculation, of which all we can say is that our ideas are spontaneous and universal,—much more must we abstain from such barren and vicious systematizing in logical researches, properly so called. Thus are the logical and scientific points of view to be finally regarded as correlative and indivisible aspects of each positive theory, neither being in reality more susceptible than the other of an abstract and general appreciation, independent of any determinate manifestation. Thus they have been treated throughout this work, in which the logical training has always coexisted with the scientific, and their connection being such that the scientific results of one science have often been found to be the logical resources of another; a fact which shows the impossibility of separating them.

Relations

Thus have we ascertained the composition of the positive method: and we have only further to mark out the systematic co-ordination of the chief successive phases which it of phases. has naturally presented.

Mathematics.

No irrational exaggeration of the claims of Mathematics can ever deprive that part of philosophy of the property of being the natural basis of all logical education, through its simplicity, abstractness, generality, and freedom from disturbance by human passion. There, and there alone, we find in full development the art of reasoning, all the resources of which, from the most spontaneous to the most sublime, are continually applied with far more variety and fruitfulness than elsewhere; whereas the art of observation, though there receiving its first scientific application, is scarcely traceable, even in mechanics. The more abstract portion of mathematics may in fact be regarded as an immense repository of logical resources, ready for use in scientific deduction and co-ordination: yet, as the human mind is indisposed to the most abstract speculation, it is geometry, rather than analysis, that will always be, in a logical view, the chief of the three branches of mathematics, and the fittest for the first elaboration of the positive method. When Descartes chose geometry for the ground of his organization of the relation of the abstract to the concrete, he made it the centre of mathematical conceptions, as analysis found there vast material and a noble application, in return for the generality which it imparted. Mechanics, on the contrary, though yet more important than geometry, in a scientific view, has by no means the same logical value, on account of its greater complexity; and the obligations of analysis to it are but secondary and indirect. In passing from geometrical to dynamical speculations, we feel how near we are to the limits of the mathematical province, from the extreme difficulty of treating the

simplest questions in a thoroughly satisfactory manner.-We have seen abundant reasons, in the course of our survey, why the mind that confines itself within the mathematical province is subject to a variety of fatal snares, and very ill prepared for the loftiest aims of human reason. Without recapitulating the faults and errors arising from the misuse of the mathematical spirit, it is enough to say that when a sound philosophy prevails, it will be felt that the first phase of positive logic not only cannot dispense with those which follow, but must look to them for much reactive assistance from their combination, without which mathematical logic itself cannot be completely understood and valued.

These considerations show us the value of the next phase, the astronomical, in which the positive method obtains a Astronomy. second degree of development, in the closest connection with the first. It is overlaid, as we have seen, with mathematical ideas and procedures; but, discarding these as far as possible, we shall find that the distinction, logical and scientific, between this phase and the last is much greater than is commonly supposed. In geometry, the disproportion between the observation employed and the consequences obtained is so great as to render the function of observation almost inappreciable: whereas, in astronomy it is distinct and direct. Here, as the simplest and most general of the four resources for obtaining knowledge, it shows what may be done, in the most unfavourable situation, by a single sense in ascertaining the most intellectual kind of truth. Not less striking is the intervention of the logical processes which here guide an investigation singularly indirect: and thus if, in a scientific view, astronomy is fairly regarded as the most fundamental part of the system of inorganic knowledge, it is no less, in a logical view, the most perfect type of the general study of nature. Here men learned to modify the earliest philosophy by conceptions derived from the study of the external world; and here we find the fittest dogmatic exposition of rational positivity. Here, throughout all time, will be found the first philosophical sense of natural law; and here may be learned what is meant by the explanation of any phenomenon, by means of resemblance or connection. The whole of its historical and dogmatic course discloses the agreement between our conceptions and our observations which is the essential character of real knowledge. It yields us the true theory of scientific hypotheses; and it proves that its rationality is not less satisfactory than its positivity, by offering the first and most perfect example, thus far indeed the only one, of that rigorous philosophical unity which must be kept in view in every order of speculation. No other science, again, has so familiarly manifested that rational prevision which is the most marked characteristic of positive theory. Its imperfections proceed from a want of definiteness in the circumscription of the objects and the subjects of its researches; an imperfection which time will cure.